Question

question 13 (mandatory) (1 point)
in △abc, a = 5.4 m, b = 7.2 m, and c = 10.0 m. determine ∠c to the nearest degree.

a) 97°
b) 92°
c) 104°
d) 108°

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). Rearranging for \(\cos C\) gives \(\cos C=\frac{a^{2}+b^{2}-c^{2}}{2ab}\).
Substitute \(a = 5.4\), \(b = 7.2\), and \(c = 10.0\) into the formula:
\(\cos C=\frac{5.4^{2}+7.2^{2}-10.0^{2}}{2\times5.4\times7.2}\)
First, calculate the numerator: \(5.4^{2}=29.16\), \(7.2^{2}=51.84\), \(10.0^{2} = 100\).
\(29.16+51.84 - 100=81 - 100=-19\)
The denominator is \(2\times5.4\times7.2 = 77.76\)
So, \(\cos C=\frac{-19}{77.76}\approx - 0.2443\)

Step2: Find the angle \(C\)

Since \(C=\cos^{-1}(-0.2443)\)
Using a calculator, \(C\approx104^{\circ}\)

Answer:

C. \(104^{\circ}\)